Company XYZ knows that replacement times for the quartz time pieces it produces are normally distributed with a mean of 12.5 years and a standard deviation of 0.6 years.

Question

Company XYZ knows that replacement times for the quartz time pieces it produces are normally distributed with a mean of 12.5 years and a standard deviation of 0.6 years.

(a) Find the probability that a randomly selected quartz time piece will have a replacement time less than 11.2 years. Give the probability rounded to 4 places after the decimal. 

P(X < 11.2 years) = 

(b) If the company wants to provide a warranty so that only 4.1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? Give the length in years, rounded to one decimal place.

Warranty length =  years

Answer 1

P(X < 11.2 years) = .0151

Warranty length = 13.5 years